Logical Organisation of Computer
Venn Diagram:- Venn diagram uses overlapping circles or other shapes to illustrate the logical relationship between two or more sets of items.
DUALITY PRINCIPLE:-
In Boolean algebra there is a precise (fine) duality between the operators AND and OR and the digits 0 and 1. For illustrate, let us consider Table here second row is obtained from first row simply By interchanging + with . and 0 with 1. This important property is known as the principle of duality in Boolean algebra.
PARALLEL ADDER:-
A digital circuit that is used to add two binary numbers using Full Adder known as Parallel Adder. It is a digital circuit that is efficient to add more than 1 bit binary numbers. Parallel Adders are implemented using Full Adders.
It consists of carry bit and sum bit after performing addition of two binary input bits.
For example if we want to construct a four-bit or value then, we need to construct a four-bit Binary Parallel Adder as shown in figure.
BCD TO 7 SEGMENT DECODER:-
BCD to 7 segment decoder is the most popular display device used in digital systems. To use the display device the data which is in the BCD format has to be changed suitably.
In this decoder the outputs are used to drive seven segments (a b c d e f g).
Digital systems such as computers, calculators, watches etc use BCD numbers which are converted into seven segment codes with the help of combinational logic circuits. The seven segment A to G are shown in fig;-
ENCODER:-
An Encoder is a combinational circuit that performs the reverse operation of Decoder. It has a maximum of 2n input lines and ‘n’ output lines. It requires 2^n input lines and n outputs line.
It is used to encode Octal, Decimal, Hexadecimal code to binary code.
For example if we have 2^n=m,
2^3=8
Here 3 is outpups and 8 is inputs.
DECODER:-
A decoder is a device which can Decode a binary value into their equivalent codes like; Octal Code, Decimal Code, Hexadecimal Code etc.
It is a Combinational circuit which converts the binary information from n input lines to maximum of 2n output lines.
For example if we have 2^n=m,
2^3=8
Here 8 is outpups and 3 is inputs.
MULTILEVEL NAND AND NOR GATE:-
NOT, AND and OR gate are logically complete because we can express any Boolean expression using these three Basic gates. However, NAND and NOR gate are universal gates; it is alone sufficient to express any Boolean expression.
Multilevel circuits consisting of AND , OR and NOT gate can be easily converted into circuits that can be realized with NAND and NOR gate. An AND-OR ( sum of product) circuit can be realized using a NAND-NAND circuit similarly, a OR-AND ( product of sum) circuit can be realized using NOR-NOR circuit. This conversation is called Multilevel NAND and NOR circuit.
Steps or Procedure:-
Simplify the switching function to be realized.
Design a multilevel Circuit of AND and OR gates.
The Output must be OR (In case of OR-AND gates output must be AND)
Replace all gates with NAND gates. (In case of OR-AND gates replace all gates with NOR gate)
Eg;- A.B’+C(A+B.D)
MULTIPLEXER/ Data Selector:-
The multiplexer or MUX is a digital switch, also called a data selector.
Multiplexer means many to one. Multiplexer can be defined as a logic circuit that accepts many inputs but generates only one output. The input selected is controlled by a set of selection lines.
Thus, Multiplexer is that logic circuit which receives binary data in 2^n input lines and directs it to a single output line selected by a set of n selection lines.
The basic function of a multiplexer is combining multiple inputs into a single data stream which helps in reducing cost of communication system.
Application of Multiplexer:-
Main applications of multiplexers in digital systems are data routing, data selection, parallel to serial conservation, operation sequencing, waveform generation and logical function generation.
as a data selected to select one out of many data inputs.
Mux Can be used to implement combinational logic circuits.
Mux are used in time multiplexing systems.
Mux are used in frequency multiplexing systems.
Mux used in A/D and D/A converters. They are used in data acquisition systems.
DEMULTIPLEXER/ Data Distributor:-
Demultiplexer or Demux is a digital circuit also called Data Distributor.
Demultiplexer one into many. Therefore, a demultiplexer or data distributor can be defined as a logic circuit that accepts only one input and generates many outputs. The set of select inputs determines to which output the data input will be transmitted.
Demultiplexer performs the reverse operation of a multiplexer. Thus, a demultiplexer is the logic circuit which receives one input by applying n control input or select inputs and transfer the input signal to one of the 2^n output lines.
COMBINATIONAL AND SEQUENTIAL CIRCUIT:-
Combinational circuits are defined as the time independent circuits which do not depends upon previous inputs to generate any output. It works on present inputs and present outputs. Combinational circuit doesn't have a memory and feedback element.
Speed is fast.
It is designed easy.
There is no feedback between input and output.
This is time independent.
Elementary building blocks: Logic gates
Used for arithmetic as well as boolean operations.
Combinational circuits don’t have capability to store any state.
As combinational circuits don’t have feedback elements.
These circuits do not have any memory element.
Examples – Encoder, Decoder, Multiplexer, Demultiplexer etc.
Sequential circuits are those which are dependent on clock cycles and depends on present as well as past inputs to generate any output.
In this output depends upon present as well as past input.
Speed is slow.
Hard to design as compared to combinational circuits.
Sequential circuits have a feedback path between input and output.
This is time dependent.
Elementary building blocks: Flip-flops
Mainly used for storing data.
Sequential circuits have capability to store any state or to retain earlier state.
As sequential circuits are clock dependent they need triggering.
These circuits have a memory element.
It is not easy to use and handle.
Examples – Flip-flops, Counters, Register etc.
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